For you to explain this to me, I figure you should probably already be familiar with it, so I won't go into detail. However I'll give a short synopsis (and yes I became interested in the problem because of the scene in the movie 21
but I have researched it beyond that and it still makes my head hurt).
You're on a game show. Before you are three doors. Behind one of the doors is a car and behind the other two: goats. You're asked to select a door. [I want to add here that I fully understand that whatever choice you make at this point, your chance of being correct is 33.3 percent.]
Now, you've made your choice, It is at this point that you realize a new condition: the game show host is cognizant of the car's location. He decides to open one of the doors that houses a goat. So, there were three options, one winning and two losing. However the host has eliminated one of the losing options. You now have one winning and one losing selection left.
The 'solution' to the problem is now that the host has revealed the location of one of the losing selections, it's in your interest to switch (e.g. if you pick door 1, he reveals door 3 to be a goat, it's in your interest to switch from 1 to 2). This is what I don't understand. According to Wikipedia a lot of people were flabbergasted like me that you had a better chance by switching (as apparently switching increases your odds to 66.7 percent). I understand that I'm wrong but not how I'm wrong.
I had a 33.3 percent chance. One of the wrong choices was eliminated, so there's now one winning and one losing proposition. Why is it not 50 percent regardless of whether or not I switch?
My brain is so fried right now. I've read the Wiki page a couple of times now and my mind is just numb. I'm going to go take a walk or something.D: